Alan Weir
- Published in print:
- 2010
- Published Online:
- January 2011
- ISBN:
- 9780199541492
- eISBN:
- 9780191594915
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199541492.003.0010
- Subject:
- Philosophy, Philosophy of Language, Logic/Philosophy of Mathematics
This chapter summaries the key thesis of the book: that, given the Sense/Circumstance/World framework in the philosophy of language, we can show that mathematics expresses objective truths, but not ...
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This chapter summaries the key thesis of the book: that, given the Sense/Circumstance/World framework in the philosophy of language, we can show that mathematics expresses objective truths, but not by dint of delineating a mind-independent reality. Neo-formalism is held to incorporate sound aspects of rival views, such as classic formalism; neo-logicism, in the idea that stipulation of axioms grounds mathematical truth; constructivism, insofar as the constructivist links truth with provability; strict finitism to the extent that the strict finitist emphasizes that the ontology of mathematics can include only a finite corpus of concrete tokens. Neo-formalism even incorporates elements of platonism, insofar as it upholds the objectivity of mathematical truth. However neo-formalism, in rejecting the platonistic realm of an external mathematical ontology as a mythological projection of human activity, avoids the crippling metaphysical and epistemological problems of platonism.Less
This chapter summaries the key thesis of the book: that, given the Sense/Circumstance/World framework in the philosophy of language, we can show that mathematics expresses objective truths, but not by dint of delineating a mind-independent reality. Neo-formalism is held to incorporate sound aspects of rival views, such as classic formalism; neo-logicism, in the idea that stipulation of axioms grounds mathematical truth; constructivism, insofar as the constructivist links truth with provability; strict finitism to the extent that the strict finitist emphasizes that the ontology of mathematics can include only a finite corpus of concrete tokens. Neo-formalism even incorporates elements of platonism, insofar as it upholds the objectivity of mathematical truth. However neo-formalism, in rejecting the platonistic realm of an external mathematical ontology as a mythological projection of human activity, avoids the crippling metaphysical and epistemological problems of platonism.
Martin Kusch
- Published in print:
- 2002
- Published Online:
- January 2005
- ISBN:
- 9780199251223
- eISBN:
- 9780191601767
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199251223.001.0001
- Subject:
- Philosophy, Metaphysics/Epistemology
Knowledge by Agreement defends the ideas that knowledge is a social status (like money, or marriage), and that knowledge is primarily the possession of groups rather than individuals. ...
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Knowledge by Agreement defends the ideas that knowledge is a social status (like money, or marriage), and that knowledge is primarily the possession of groups rather than individuals. Ch. 1–6 develop a new theory of testimony. They break with the traditional view according to which testimony is not, except accidentally, a generative source of knowledge. One important consequence of the new theory is a rejection of attempts to globally justify trust in the words of others. Ch. 7–12 propose a communitarian theory of empirical knowledge. It is argued that empirical belief can acquire the status of knowledge only by being shared with others, and that all empirical beliefs presuppose social institutions. As a result all knowledge is essentially political. Ch. 13–20 defend some of the controversial premises and consequences of Chs 1–12: the community‐dependence of normativity, epistemological and semantic relativism, and anti‐realism, and a social conception of objectivity.Less
Knowledge by Agreement defends the ideas that knowledge is a social status (like money, or marriage), and that knowledge is primarily the possession of groups rather than individuals. Ch. 1–6 develop a new theory of testimony. They break with the traditional view according to which testimony is not, except accidentally, a generative source of knowledge. One important consequence of the new theory is a rejection of attempts to globally justify trust in the words of others. Ch. 7–12 propose a communitarian theory of empirical knowledge. It is argued that empirical belief can acquire the status of knowledge only by being shared with others, and that all empirical beliefs presuppose social institutions. As a result all knowledge is essentially political. Ch. 13–20 defend some of the controversial premises and consequences of Chs 1–12: the community‐dependence of normativity, epistemological and semantic relativism, and anti‐realism, and a social conception of objectivity.
Alan Weir
- Published in print:
- 2010
- Published Online:
- January 2011
- ISBN:
- 9780199541492
- eISBN:
- 9780191594915
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199541492.003.0007
- Subject:
- Philosophy, Philosophy of Language, Logic/Philosophy of Mathematics
This chapter attempts to carry out the task promised earlier: a purely concretist syntax and proof theory, where abstract types are replaced by concrete ‘tipes’, construed as fusions of concrete ...
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This chapter attempts to carry out the task promised earlier: a purely concretist syntax and proof theory, where abstract types are replaced by concrete ‘tipes’, construed as fusions of concrete tokens. The conclusion is drawn that there are only finitely many sentences and proofs in actual human languages, and since no appeal to possibility beyond everyday uncontentious uses is made this seems to drive us towards a strict finitism. In particular, how can those concrete utterances which, given limits on the size of graspable proofs, can have no concrete proof or disproof, have determinate truth values? Recourse to ‘in principle possibility’ and idealized beings is rejected as no more acceptable in this domain than appeal to supernatural beings is in biology. A different model of idealization is needed.Less
This chapter attempts to carry out the task promised earlier: a purely concretist syntax and proof theory, where abstract types are replaced by concrete ‘tipes’, construed as fusions of concrete tokens. The conclusion is drawn that there are only finitely many sentences and proofs in actual human languages, and since no appeal to possibility beyond everyday uncontentious uses is made this seems to drive us towards a strict finitism. In particular, how can those concrete utterances which, given limits on the size of graspable proofs, can have no concrete proof or disproof, have determinate truth values? Recourse to ‘in principle possibility’ and idealized beings is rejected as no more acceptable in this domain than appeal to supernatural beings is in biology. A different model of idealization is needed.
Neil Tennant
- Published in print:
- 2002
- Published Online:
- October 2011
- ISBN:
- 9780199251605
- eISBN:
- 9780191698057
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199251605.003.0005
- Subject:
- Philosophy, Logic/Philosophy of Mathematics, Philosophy of Language
This chapter shows how to find an acceptable reading of knowability-in-principle in order to avoid visiting upon oneself and one's opposition the overly restrictive consequence that only the ...
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This chapter shows how to find an acceptable reading of knowability-in-principle in order to avoid visiting upon oneself and one's opposition the overly restrictive consequence that only the practically and feasibly knowable can feature in the anti-realist's manifestation requirement on grasp meaning. It discusses the strict finitist's concern about knowability-in-principle, recognitional capacities and compositionality, and feasible verifiability. It also analyses and concept of aspectual recognition and discusses ways of finding the right dispositional conditionals.Less
This chapter shows how to find an acceptable reading of knowability-in-principle in order to avoid visiting upon oneself and one's opposition the overly restrictive consequence that only the practically and feasibly knowable can feature in the anti-realist's manifestation requirement on grasp meaning. It discusses the strict finitist's concern about knowability-in-principle, recognitional capacities and compositionality, and feasible verifiability. It also analyses and concept of aspectual recognition and discusses ways of finding the right dispositional conditionals.
Mathieu Marion
- Published in print:
- 2008
- Published Online:
- September 2011
- ISBN:
- 9780199550470
- eISBN:
- 9780191701559
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199550470.003.0004
- Subject:
- Philosophy, History of Philosophy, Logic/Philosophy of Mathematics
This chapter shows that Ludwig Wittgenstein's philosophy of mathematics has much less in common with intuitionism than is usually assumed, although some strategical moves are barely distinguishable. ...
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This chapter shows that Ludwig Wittgenstein's philosophy of mathematics has much less in common with intuitionism than is usually assumed, although some strategical moves are barely distinguishable. At least one such move cannot be overlooked because of its importance for the development of Wittgenstein's philosophy: it concerns quantification theory. This chapter shows that Wittgenstein's stance on quantification was, however, even more radical than that of intuitionists. This is a topic about which Wittgenstein changed his mind around 1929. The search for the source of Wittgenstein's new ideas on quantification leads directly to Hermann Weyl. He actually developed original ideas on topics such as quantification. According to him, propositions containing an existential quantifier ranging over the natural numbers do not possess the full status of judgement.Less
This chapter shows that Ludwig Wittgenstein's philosophy of mathematics has much less in common with intuitionism than is usually assumed, although some strategical moves are barely distinguishable. At least one such move cannot be overlooked because of its importance for the development of Wittgenstein's philosophy: it concerns quantification theory. This chapter shows that Wittgenstein's stance on quantification was, however, even more radical than that of intuitionists. This is a topic about which Wittgenstein changed his mind around 1929. The search for the source of Wittgenstein's new ideas on quantification leads directly to Hermann Weyl. He actually developed original ideas on topics such as quantification. According to him, propositions containing an existential quantifier ranging over the natural numbers do not possess the full status of judgement.
Mathieu Marion
- Published in print:
- 2008
- Published Online:
- September 2011
- ISBN:
- 9780199550470
- eISBN:
- 9780191701559
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199550470.003.0005
- Subject:
- Philosophy, History of Philosophy, Logic/Philosophy of Mathematics
In order to appreciate fully the depth of Ludwig Wittgenstein's commitment to finitism, one ought to look for the causes of his change of mind on quantification. They are to be found in underlying ...
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In order to appreciate fully the depth of Ludwig Wittgenstein's commitment to finitism, one ought to look for the causes of his change of mind on quantification. They are to be found in underlying changes in the notion of analysis which took place in the first steps away from Tractatus Logico-Philosophicus in the manuscripts of 1929. Upon his return to Cambridge in January of that year, Wittgenstein immediately started writing extensively. This was a period of intense intellectual fervor. Early entries in his notebooks indicate that he had started to think afresh some of the problems even before his arrival in Cambridge and that he moved in new directions very quickly. This indicates that Wittgenstein had already given up or was about to give up one of the cental claims of the Tractatus Logico-Philosophicus.Less
In order to appreciate fully the depth of Ludwig Wittgenstein's commitment to finitism, one ought to look for the causes of his change of mind on quantification. They are to be found in underlying changes in the notion of analysis which took place in the first steps away from Tractatus Logico-Philosophicus in the manuscripts of 1929. Upon his return to Cambridge in January of that year, Wittgenstein immediately started writing extensively. This was a period of intense intellectual fervor. Early entries in his notebooks indicate that he had started to think afresh some of the problems even before his arrival in Cambridge and that he moved in new directions very quickly. This indicates that Wittgenstein had already given up or was about to give up one of the cental claims of the Tractatus Logico-Philosophicus.
Mathieu Marion
- Published in print:
- 2008
- Published Online:
- September 2011
- ISBN:
- 9780199550470
- eISBN:
- 9780191701559
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199550470.003.0008
- Subject:
- Philosophy, History of Philosophy, Logic/Philosophy of Mathematics
The philosophical world outside Cambridge discovered the later Ludwig Wittgenstein's philosophy of mathematics with the publication in the 1956 of the Remarks on the Foundations of Mathematics, a ...
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The philosophical world outside Cambridge discovered the later Ludwig Wittgenstein's philosophy of mathematics with the publication in the 1956 of the Remarks on the Foundations of Mathematics, a selection from manuscripts dating from 1938 to 1944. In his 1958 survey paper, Hao Wang promoted strict finitism, which he then called anthropologism, to the rank of a foundational thesis alongside finitism, intuitionism, predicativism, and Platonism, with the later Wittgenstein being enrolled as its most important representative. This has been by far the prevailing view ever since, with some exceptions. A useful preliminary step would be to give a brief characterization of strict finitism. Various strict finitist programmes have been devised in the past, and they do not show much homogeneity: contrary to intuitionism, there is no orthodoxy.Less
The philosophical world outside Cambridge discovered the later Ludwig Wittgenstein's philosophy of mathematics with the publication in the 1956 of the Remarks on the Foundations of Mathematics, a selection from manuscripts dating from 1938 to 1944. In his 1958 survey paper, Hao Wang promoted strict finitism, which he then called anthropologism, to the rank of a foundational thesis alongside finitism, intuitionism, predicativism, and Platonism, with the later Wittgenstein being enrolled as its most important representative. This has been by far the prevailing view ever since, with some exceptions. A useful preliminary step would be to give a brief characterization of strict finitism. Various strict finitist programmes have been devised in the past, and they do not show much homogeneity: contrary to intuitionism, there is no orthodoxy.
Ilkka Niiniluoto
- Published in print:
- 2002
- Published Online:
- November 2003
- ISBN:
- 9780199251612
- eISBN:
- 9780191598098
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199251614.003.0009
- Subject:
- Philosophy, Philosophy of Science
Philosophers of science should take seriously the fact, emphasized already by Peirce and Popper, that scientific knowledge is a product of the scientific community. The ontological and ...
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Philosophers of science should take seriously the fact, emphasized already by Peirce and Popper, that scientific knowledge is a product of the scientific community. The ontological and epistemological views associated with the sociology of science have often been interpreted as forms of relativism and anti‐realism. This chapter examines critically the position of the Edinburgh school (Bloor, Barnes). It is argued that the Strong Programme need not be in conflict with realism, but its radically nominalist doctrine of meaning finitism should be rejected. But Latour's social constructivism, if taken literally as an ontological view, cannot be reconciled with scientific realism.Less
Philosophers of science should take seriously the fact, emphasized already by Peirce and Popper, that scientific knowledge is a product of the scientific community. The ontological and epistemological views associated with the sociology of science have often been interpreted as forms of relativism and anti‐realism. This chapter examines critically the position of the Edinburgh school (Bloor, Barnes). It is argued that the Strong Programme need not be in conflict with realism, but its radically nominalist doctrine of meaning finitism should be rejected. But Latour's social constructivism, if taken literally as an ontological view, cannot be reconciled with scientific realism.
Martin Kusch
- Published in print:
- 2002
- Published Online:
- January 2005
- ISBN:
- 9780199251223
- eISBN:
- 9780191601767
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199251223.003.0016
- Subject:
- Philosophy, Metaphysics/Epistemology
Meaning finitism is a communitarian theory of what it is to master a language. It makes community consensus central in the constitution of normativity. Finitism says that terms have no fixed ...
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Meaning finitism is a communitarian theory of what it is to master a language. It makes community consensus central in the constitution of normativity. Finitism says that terms have no fixed extensions. The only extensions there are the ’pseudo‐extensions’ of arrays of exemplars concerning correct use. The categorization of newly‐encountered entities is guided by these exemplars, as well as by interests.Less
Meaning finitism is a communitarian theory of what it is to master a language. It makes community consensus central in the constitution of normativity. Finitism says that terms have no fixed extensions. The only extensions there are the ’pseudo‐extensions’ of arrays of exemplars concerning correct use. The categorization of newly‐encountered entities is guided by these exemplars, as well as by interests.
Martin Kusch
- Published in print:
- 2002
- Published Online:
- January 2005
- ISBN:
- 9780199251223
- eISBN:
- 9780191601767
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199251223.003.0017
- Subject:
- Philosophy, Metaphysics/Epistemology
Applies finitism to ’true’ and ’false’. Applying finitism to truth leads to radical and surprising consequences. If ’true’ does not have a fixed extension, then it is simply incoherent to speak of, ...
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Applies finitism to ’true’ and ’false’. Applying finitism to truth leads to radical and surprising consequences. If ’true’ does not have a fixed extension, then it is simply incoherent to speak of, or tacitly rely on, the idea of ’all true statements’ (or ’all true propositions’, or ’all true beliefs’, or ’all true sentences’). And if this idea is illegitimate, then so are traditional ways of thinking about scientific progress (’we are getting ever closer to the truth’). The finitistic theory of meaning constitutes an important constraint on all theories of truth. The finitistic constraint rules out theories of truth that make use of fixed extensions.Less
Applies finitism to ’true’ and ’false’. Applying finitism to truth leads to radical and surprising consequences. If ’true’ does not have a fixed extension, then it is simply incoherent to speak of, or tacitly rely on, the idea of ’all true statements’ (or ’all true propositions’, or ’all true beliefs’, or ’all true sentences’). And if this idea is illegitimate, then so are traditional ways of thinking about scientific progress (’we are getting ever closer to the truth’). The finitistic theory of meaning constitutes an important constraint on all theories of truth. The finitistic constraint rules out theories of truth that make use of fixed extensions.
Martin Kusch
- Published in print:
- 2002
- Published Online:
- January 2005
- ISBN:
- 9780199251223
- eISBN:
- 9780191601767
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199251223.003.0018
- Subject:
- Philosophy, Metaphysics/Epistemology
Reviews the contemporary debate between realists (’innocent’, ’external’, ’absolute’, ’metaphysical’) and anti‐realists (’irrealism’, ’internal realism’, ’pluralism’, ’relativistic Kantianism’). ...
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Reviews the contemporary debate between realists (’innocent’, ’external’, ’absolute’, ’metaphysical’) and anti‐realists (’irrealism’, ’internal realism’, ’pluralism’, ’relativistic Kantianism’). Criticises ideas and arguments of both sides of the debate where they were based on mistaken semantic assumptions (of fixed extensions). In particular, the chapter rejects the notion of ’one true description of the world’, talk of ’determinate meanings and truth values within a conceptual scheme’, and the idea of once‐and‐for‐all incompatibilities between conceptual schemes.Less
Reviews the contemporary debate between realists (’innocent’, ’external’, ’absolute’, ’metaphysical’) and anti‐realists (’irrealism’, ’internal realism’, ’pluralism’, ’relativistic Kantianism’). Criticises ideas and arguments of both sides of the debate where they were based on mistaken semantic assumptions (of fixed extensions). In particular, the chapter rejects the notion of ’one true description of the world’, talk of ’determinate meanings and truth values within a conceptual scheme’, and the idea of once‐and‐for‐all incompatibilities between conceptual schemes.
Alexander R. Pruss
- Published in print:
- 2018
- Published Online:
- September 2018
- ISBN:
- 9780198810339
- eISBN:
- 9780191847325
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198810339.003.0010
- Subject:
- Philosophy, Metaphysics/Epistemology, Philosophy of Science
The upshot of the preceding nine chapters is briefly summarized and discussed, offering a view of causal finitism as a via media between finitism and infinitism.
The upshot of the preceding nine chapters is briefly summarized and discussed, offering a view of causal finitism as a via media between finitism and infinitism.
Paolo Mancosu
- Published in print:
- 2010
- Published Online:
- May 2011
- ISBN:
- 9780199546534
- eISBN:
- 9780191594939
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199546534.003.0008
- Subject:
- Philosophy, Logic/Philosophy of Mathematics, Philosophy of Mind
This chapter is an essay review of volumes IV and V of Gödel’s Collected Works. Here the aim is to study the heuristics that led to Gödel’s incompleteness theorems by making use of the correspondence ...
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This chapter is an essay review of volumes IV and V of Gödel’s Collected Works. Here the aim is to study the heuristics that led to Gödel’s incompleteness theorems by making use of the correspondence contained in volumes IV and V and to argue that knowledge of the correspondence deepens our understanding of various aspects of the theorems ranging from the role of “truth” and “provability” to specific details of how Gödel gives an exposition of his result in his groundbreaking 1931 article. The chapter also studies the different reactions to Gödel’s incompleteness theorem by Gödel and Bernays, who thought that Hilbert’s program could be salvaged, and those of von Neumann and Herbrand, who saw the result as showing once and for all that Hilbert’s program could not be carried out.Less
This chapter is an essay review of volumes IV and V of Gödel’s Collected Works. Here the aim is to study the heuristics that led to Gödel’s incompleteness theorems by making use of the correspondence contained in volumes IV and V and to argue that knowledge of the correspondence deepens our understanding of various aspects of the theorems ranging from the role of “truth” and “provability” to specific details of how Gödel gives an exposition of his result in his groundbreaking 1931 article. The chapter also studies the different reactions to Gödel’s incompleteness theorem by Gödel and Bernays, who thought that Hilbert’s program could be salvaged, and those of von Neumann and Herbrand, who saw the result as showing once and for all that Hilbert’s program could not be carried out.
Paolo Mancosu
- Published in print:
- 2010
- Published Online:
- May 2011
- ISBN:
- 9780199546534
- eISBN:
- 9780191594939
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199546534.003.0013
- Subject:
- Philosophy, Logic/Philosophy of Mathematics, Philosophy of Mind
Tarski, Carnap and Quine spent the academic year 1940–1941 together at Harvard. In their autobiographies, both Carnap and Quine highlight the importance of the conversations that took place among ...
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Tarski, Carnap and Quine spent the academic year 1940–1941 together at Harvard. In their autobiographies, both Carnap and Quine highlight the importance of the conversations that took place among them during the year. These conversations centred around semantical issues related to the analytic/synthetic distinction and on the project of a finitist/nominalist construction of mathematics and science. Carnap’s Nachlass in Pittsburgh contains a set of detailed notes, amounting to more than 80 typescripted pages, taken by Carnap while these discussions were taking place. This Chapter presents a survey of these notes with special emphasis on Tarski’s rejection of the analytic/synthetic distinction, the passage from typed languages to first-order languages, Tarski’s finitism/nominalism, and the construction of a finitist language for mathematics and science.Less
Tarski, Carnap and Quine spent the academic year 1940–1941 together at Harvard. In their autobiographies, both Carnap and Quine highlight the importance of the conversations that took place among them during the year. These conversations centred around semantical issues related to the analytic/synthetic distinction and on the project of a finitist/nominalist construction of mathematics and science. Carnap’s Nachlass in Pittsburgh contains a set of detailed notes, amounting to more than 80 typescripted pages, taken by Carnap while these discussions were taking place. This Chapter presents a survey of these notes with special emphasis on Tarski’s rejection of the analytic/synthetic distinction, the passage from typed languages to first-order languages, Tarski’s finitism/nominalism, and the construction of a finitist language for mathematics and science.
Stephen Welch
- Published in print:
- 2013
- Published Online:
- September 2013
- ISBN:
- 9780199553334
- eISBN:
- 9780191756009
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199553334.003.0009
- Subject:
- Political Science, Political Theory
Chapter 8 accounts for the fluidity of political culture in terms of its discursive dimension. The approach of discursivism has first to be rejected, for it assumes the invariable success of ...
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Chapter 8 accounts for the fluidity of political culture in terms of its discursive dimension. The approach of discursivism has first to be rejected, for it assumes the invariable success of discursive control. The arguments of Chapter 5 show that articulate discourse has a political reach that must always exceed its grasp. Archer’s dualistic theory of culture is found to construe discourse in an excessively abstract manner. In order to capture the causal impact of discourse the theory of ‘meaning finitism’ developed by David Bloor is deployed. This theory argues that discursive agreement creates, through social construction, new objective facts, to which action must adapt. But because these facts are supported only by mutually referring agreement, they are, like the objective conditions of the economic market, subject to unpredictable and chaotic dynamics. The analytic paradigm of the market is then applied to studies of the dynamics of political culture.Less
Chapter 8 accounts for the fluidity of political culture in terms of its discursive dimension. The approach of discursivism has first to be rejected, for it assumes the invariable success of discursive control. The arguments of Chapter 5 show that articulate discourse has a political reach that must always exceed its grasp. Archer’s dualistic theory of culture is found to construe discourse in an excessively abstract manner. In order to capture the causal impact of discourse the theory of ‘meaning finitism’ developed by David Bloor is deployed. This theory argues that discursive agreement creates, through social construction, new objective facts, to which action must adapt. But because these facts are supported only by mutually referring agreement, they are, like the objective conditions of the economic market, subject to unpredictable and chaotic dynamics. The analytic paradigm of the market is then applied to studies of the dynamics of political culture.
Alexander R. Pruss
- Published in print:
- 2018
- Published Online:
- September 2018
- ISBN:
- 9780198810339
- eISBN:
- 9780191847325
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198810339.003.0001
- Subject:
- Philosophy, Metaphysics/Epistemology, Philosophy of Science
Thomson’s Lamp gives a simple example of a paradox of infinity. Different ways of resolving a paradox in general are considered, and in particular two resolutions of Thomson’s Lamp are considered. ...
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Thomson’s Lamp gives a simple example of a paradox of infinity. Different ways of resolving a paradox in general are considered, and in particular two resolutions of Thomson’s Lamp are considered. According to finitism, there can only be finitely many things, and according to causal finitism, there can only be finitely many causes impinging on an effect. It is argued that finitism fits poorly with mathematics, requires a controversial theory of time to resolve paradoxes, and although it does resolve some additional paradoxes like Hilbert’s Hotel, it is nonetheless not preferable to causal finitism. The additional paradoxes are ones we should just live with, a part of the strangeness of infinity. Additionally, some technical background is given for the book, and a philosophy of mathematics application is given.Less
Thomson’s Lamp gives a simple example of a paradox of infinity. Different ways of resolving a paradox in general are considered, and in particular two resolutions of Thomson’s Lamp are considered. According to finitism, there can only be finitely many things, and according to causal finitism, there can only be finitely many causes impinging on an effect. It is argued that finitism fits poorly with mathematics, requires a controversial theory of time to resolve paradoxes, and although it does resolve some additional paradoxes like Hilbert’s Hotel, it is nonetheless not preferable to causal finitism. The additional paradoxes are ones we should just live with, a part of the strangeness of infinity. Additionally, some technical background is given for the book, and a philosophy of mathematics application is given.
Jan von Plato
- Published in print:
- 2017
- Published Online:
- May 2018
- ISBN:
- 9780691174174
- eISBN:
- 9781400885039
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691174174.003.0007
- Subject:
- History, History of Science, Technology, and Medicine
This chapter argues that the best-known statement of finitism is ascribed to Leopold Kronecker (1823–1891). The source of the statement is not Kronecker himself, at least not directly, but rather his ...
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This chapter argues that the best-known statement of finitism is ascribed to Leopold Kronecker (1823–1891). The source of the statement is not Kronecker himself, at least not directly, but rather his editor, Kurt Hensel. Kronecker's finitistic dictum was the basis for the philosophy of mathematics of Thoralf Skolem (1887–1963), a solitary combinatorial genius who started to work with Ernst Schröder's algebra of logic. In his work, he established many of the basic results of lattice theory, such as the independence of the axioms. He also defined what later came to be called Heyting algebras, lattices with an “arrow” operation that imitates implication, and established many basic properties.Less
This chapter argues that the best-known statement of finitism is ascribed to Leopold Kronecker (1823–1891). The source of the statement is not Kronecker himself, at least not directly, but rather his editor, Kurt Hensel. Kronecker's finitistic dictum was the basis for the philosophy of mathematics of Thoralf Skolem (1887–1963), a solitary combinatorial genius who started to work with Ernst Schröder's algebra of logic. In his work, he established many of the basic results of lattice theory, such as the independence of the axioms. He also defined what later came to be called Heyting algebras, lattices with an “arrow” operation that imitates implication, and established many basic properties.
David Hatherly, David Leung, and Donald MacKenzie
- Published in print:
- 2008
- Published Online:
- August 2013
- ISBN:
- 9780262162524
- eISBN:
- 9780262281607
- Item type:
- chapter
- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262162524.003.0005
- Subject:
- Society and Culture, Technology and Society
This chapter presents the philosophical roots of finitism, financial reporting in finitist perspective, accounting for economic reality, and rule-governed accounting. Finitism helps people in ...
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This chapter presents the philosophical roots of finitism, financial reporting in finitist perspective, accounting for economic reality, and rule-governed accounting. Finitism helps people in classifying activities, items, and states of all kinds, whereas financial statements include an income statement, a statement of financial position, and a cash flow statement. According to the authors, corporate financial reporting is a major gap in sociological understandings of contemporary economic processes. Financial reporting directly affects the economic health of corporations and economic reality has been considered as an important part of it. The authors have also explained accruals-based current financial reporting, the valuation of a company’s assets, and several approaches for the detection of earnings management.Less
This chapter presents the philosophical roots of finitism, financial reporting in finitist perspective, accounting for economic reality, and rule-governed accounting. Finitism helps people in classifying activities, items, and states of all kinds, whereas financial statements include an income statement, a statement of financial position, and a cash flow statement. According to the authors, corporate financial reporting is a major gap in sociological understandings of contemporary economic processes. Financial reporting directly affects the economic health of corporations and economic reality has been considered as an important part of it. The authors have also explained accruals-based current financial reporting, the valuation of a company’s assets, and several approaches for the detection of earnings management.
John Turri
- Published in print:
- 2014
- Published Online:
- August 2014
- ISBN:
- 9780199609598
- eISBN:
- 9780191779374
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199609598.003.0013
- Subject:
- Philosophy, Metaphysics/Epistemology
This chapter defends the unpopular view that inference can create justification. The chapter calls this view inferential creationism. Inferential creationism has been favored by infinitists, who ...
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This chapter defends the unpopular view that inference can create justification. The chapter calls this view inferential creationism. Inferential creationism has been favored by infinitists, who think that it supports infinitism. But it doesn’t. Finitists can and should accept creationism.Less
This chapter defends the unpopular view that inference can create justification. The chapter calls this view inferential creationism. Inferential creationism has been favored by infinitists, who think that it supports infinitism. But it doesn’t. Finitists can and should accept creationism.
Denis Bonnay
- Published in print:
- 2018
- Published Online:
- July 2018
- ISBN:
- 9780190690649
- eISBN:
- 9780190690670
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780190690649.003.0010
- Subject:
- Philosophy, Philosophy of Science
Philosophy of mathematics deals both with ontological issues (what is it that mathematics studies?) and epistemological issues (how is mathematical knowledge possible?). This chapter reviews the main ...
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Philosophy of mathematics deals both with ontological issues (what is it that mathematics studies?) and epistemological issues (how is mathematical knowledge possible?). This chapter reviews the main answers given to these two sets of issues, stressing how interrelated they are. It starts from the classical opposition between empiricist, rational, and critical approaches to set the sage and poses the question of mathematics’ relationship with experience as well as the one of the respective roles of intuition and logical principles. A detailed account of two anti-realist programs (finitism and intuitionism) is provided. Arguments in favor of realism are presented, and distinct realist views are distinguished. Having confronted the epistemological difficulties of various realist views, the last part of the chapter deals with naturalist perspectives and mathematical structuralism.Less
Philosophy of mathematics deals both with ontological issues (what is it that mathematics studies?) and epistemological issues (how is mathematical knowledge possible?). This chapter reviews the main answers given to these two sets of issues, stressing how interrelated they are. It starts from the classical opposition between empiricist, rational, and critical approaches to set the sage and poses the question of mathematics’ relationship with experience as well as the one of the respective roles of intuition and logical principles. A detailed account of two anti-realist programs (finitism and intuitionism) is provided. Arguments in favor of realism are presented, and distinct realist views are distinguished. Having confronted the epistemological difficulties of various realist views, the last part of the chapter deals with naturalist perspectives and mathematical structuralism.
